GMAT question - symantic problem?

[madnak]

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I agree it's poorly worded, but it's incorrect to use the 720 interpretation. The question said nothing about pairs of digits, so you have no reason to disallow pairs of digits.

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The question implies that all three digits are unequal. This disallows pairs.

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If the order of digits in the entries matters, how many different possible entries exist in which all three digits are different?


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This is what they would have asked if they were looking for 10*9*8.

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"Different" and "not equal" are close enough.

[Philo]

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This was in a GMAT book, and I think the wording is a little ambiguous. I can see how to get two answers depending on how I read it. Thoughts?

Entries in a particular lottery game are made up of three digits, each 0 through 9. If the order of digits in the entries matters, how many different possible entries exist in which all three digits are not equal?

[ ]516
[ ]720
[ ]989
[ ]990
[ ]1321

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Yes, the question is ambiguous. The ambiguity is in the scope of the negation (called a 'scope ambiguity'), which is a common error for students learning logic. The sentence "How many different possible entries exist in which all three digits are not equal?" is ambiguous between (1) How many different possible entries exist in which it is not the case that all three digits are the same digit?; and (2) How many different possible entries exist in which it is not the case that any two digits are the same digit? If you read the question the first way the answer is 990, while if you read the the second way the answer is 720.

Unfortunately many standardized tests are poorly written. The GRE, the LSAT, the GMAT, all often contain poorly written questions. For those who can spot the ambiguities and otherwise poorly written questions the only way to get good at taking these tests is to develop a feel for which question is actually being intended. Many IQ tests are also very poorly written.

I once took a multiple choice exam in a psychology class where one question had one answer choice that was what our textbook said was the right answer, and another answer choice that was the actual correct answer. Knowing the textbook was wrong I chose the actual correct answer, and when it was marked as wrong when I got the test back I asked the professor why, pointing out that the textbook was wrong. His reply was, 'I know, but I was testing you on the book."

[stinkypete]

imo 990 is the only correct way to interpret this, but i agree that the wording is stupid if that's not what they're trying to screw you on - since this is on the quant part, the wording should be more clear.

the test will likely not be that retarded. test prep book makers are just out to make some monies and the quality control can be pretty atrocious.

[Sephus]

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Knowing the textbook was wrong I chose the actual correct answer, and when it was marked as wrong when I got the test back I asked the professor why, pointing out that the textbook was wrong. His reply was, 'I know, but I was testing you on the book."

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the play here is to punch him in the face.

[madnak]

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imo 990 is the only correct way to interpret this

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The 720 grammar is perfectly correct and less convoluted.

[luckyme]

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The sentence "How many different possible entries exist in which all three digits are not equal?" is ambiguous between (1) How many different possible entries exist in which it is not the case that all three digits are the same digit?; and (2) How many different possible entries exist in which it is not the case that any two digits are the same digit?

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I read the question as "How many different possible entries exist in which all three digits ARE equal?"
Then I took the the 'not' as meaning "all the other cases".
Obviously too simplistic, but I can't quite figure out why.

luckyme

[madnak]

The problem here is the adverb "not." It can modify either the verb "are" or the adjective "equal." Logically the former case gets you "the digits not (are equal)," the latter gets you "the digits are (not equal)." This is like the "spinning dancer" problem, people interpret it differently.

In the 990 case "not" and "equal" both modify "are." When "not" modifies the main verb, we can usually apply it to the whole sentence. The clause in this case. Applying "not" to the clause yields "it's not the case that the digits are equal." In the 770 case it's easy to avoid the adverb - substitute "not equal" for "unequal" and we get "the digits are unequal."

("All three" is redundant - I leave it out because the writer should have done the same.)

These situations are one reason why good writers avoid adverbs whenever possible. It also helps explain some stylistic conventions - "cannot" is clearer than "can not" because it prevents this sort of ambiguity.

[stinkypete]

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imo 990 is the only correct way to interpret this

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The 720 grammar is perfectly correct and less convoluted.

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i'm not gonna argue about correct but it's definitely not less convoluted imo.

[madnak]

Eh, convolution is subjective. But all I have to do is change "not equal" to "unequal" and I've fixed the 720 version. Can you fix the 990 version without restructuring the sentence?

"Aren't" instead of "are not" makes the 990 interpretation more intuitive, but doesn't solve the problem. I can't think of any other simple fixes.

[Philo]

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imo 990 is the only correct way to interpret this,

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If the question is ambiguous there cannot be only one correct way to interpret it.